Well, wait, I think we need to step back. (controlling urge to quote Real Genius....)
If the APH rate doesn't show for your dates, it isn't available at that time for your dates. As far as I know there's no "all the time" AP discount that you can just *get* when you arrive.
When you call and ask for the APH rate, or when you go online to the Loews site and put in APH, and there's NO AP rate given, then there's no AP rate for those dates to be had at that time.
There might have been AP rates, there might be AP rates in the future. But not right then.
It's never recommended to get an AP and THEN try for the rates, if the rates are the only reason you want the AP. If the AP is the only reason, first you try and try and try to get an AP rate, and IF you do, then you buy the AP.
But for the time being, book the lowest rate that you see that you can deal with paying if no AP rate ever shows up, and if the AP rate shows up later on, you can switch it.
OP, we booked an AP rate for our second Universal trip, simply using APH in the code box online. I bought an AP online AFTER that, because the total price made sense. (the savings with the AP rate was more than me upgrading from tickets to APs) I had the voucher with me to show at checkin. Now, they never asked for it, but that's beside the point; they could have, and I had it, but I didn't even have an AP in hand when I checked in, and they didn't care.
Your first TM was wrong.
But there's no blanket AP rate you'll get just by having one. The APH rate has to be booked, in order to get it.
This site is lovely for checking all three hotels at once. Just pop in APH to the code box, and if an AP rate shows up, book it. If not, go for the lowest rate you are shown, if you will be staying there no matter what.
And then do what I do...check every day for that APH rate to show up!
As an illustration, I just put in 3/28 through 3/31 of this year, and for two hotels (just now) there is an AP rate available. For the third hotel, it's only a seasonal rate. Go look, see the difference (if it's still there when you look).